SALT LAKE CITY — GOP Gov. Gary Herbert holds a commanding lead over his Democratic challenger, Peter Cooke, in a new Deseret News/KSL poll.

Sixty-nine percent of Utah voters surveyed said they support Herbert's bid for his first full term as governor, while 24 percent back Cooke, a retired Army general with limited political experience. Five percent of the respondents said they were undecided.

The statewide poll of 870 registered voters was conducted Oct. 26-Nov. 1 by Dan Jones and Associates and has a margin of error of plus or minus 3.4 percent.

"It's encouraging," Herbert said Friday during a break on the campaign trail. "I think it means our message is resonating with the people. I think they like what we've been able to accomplish. But we're going to continue to work hard through Election Day."

Attorney general candidate John Swallow in Salt Lake City on Thursday, June 14, 2012. (Jeffrey D. Allred, Deseret News)

The governor said voters are responding to "the fact that the state of Utah is having some really great successes on my watch," particularly when it comes to weathering the nation's economic downturn.

Still, Herbert said, the support "doesn't mean things are perfect. It doesn't mean we don't have challenges."

Cooke said he couldn't pinpoint why he was behind in poll.

"It is what it is," he said. "There are so many factors this year, it's hard to indicate which ones" are affecting the race. Having Mitt Romney, a GOP presidential candidate with strong Utah ties, at the top of the ticket is "a huge, huge factor," he said.

Despite the deficit in the poll, Cooke said he wasn't slowing down his campaign efforts.

Pollster Dan Jones said Herbert is a formidable foe because of he's well-known and well-liked by Utahns. Herbert assumed the governorship in 2009 after former Gov. Jon Huntsman Jr. stepped down to be U.S. ambassador to China.

Herbert handily won the 2010 special election for the remainder of Huntsman's term.

The governor's popularity "would be very difficult for anyone running this year to upset," Jones said, especially with Romney on the ballot.

"Peter Cooke has worked very, very hard, but it's just a very, very difficult year for Democrats," he said.

In the Utah attorney general's race, Republican John Swallow has a sizable lead over Democratic Weber County Attorney Dee Smith, 55 percent to 24 percent. Another 18 percent are undecided, while 3 percent favor another candidate. Libertarian Andrew W. McCullough is the only third-party candidate in the race.